1. Field of the Invention
This invention relates generally to the field of object modeling, and, more specifically, to representing a surface of an object through a mesh of polygons, and performing operations such as trimming operations on the surface representation.
2. Related Art
In the area of computer aided geometric design (CAGD), an object surface is sought to be manufactured from a representation of the object surface. Because the manufactured surface is often subject to very tight tolerances, it is critical that the object representation be as accurate as possible. Unfortunately, for several reasons, current object modeling techniques, such as tensor product NURBS (non-uniform rational B-splines), are often unable to achieve the required numerical precision.
First, NURBS methods can represent surfaces of arbitrary topology only by partitioning the object representation into a collection of individual NURBS patches. Adjacent patches must then be explicitly stitched together using geometric continuity conditions. This requires careful patch layout and cumbersome cross boundary continuity management to build complex shapes. This practice is particularly cumbersome in computer animation, where it often leads to the appearance of kinks and cracks, especially when such patch complexes are animated.
A second problem with NURBS is in the context of trimming operations, that is, operations in which an object representation is cut along a prescribed border or trim curve to, for example, insert a rivet hole. To trim a NURBS patch, the specified area in the representation to be trimmed is typically not altered. Instead, the specified area bounded by the trim curve is represented in the parametric domain. This parametric representation of the bounded area is then retained during the manufacturing process to ensure that the prescribed area is left unfilled. Unfortunately, a parametric representation of a trim curve is often prohibitively difficult to achieve with precision. Consequently, topological inconsistencies such as cracks are often introduced.
Subdivision surface modeling, in which an object surface is modeled as a mesh of polygons such as triangles, provides a means for modeling objects of arbitrary topology that may include both smooth curved surfaces and sharp edges. Unlike NURBS, the technique does not require the use of separate patches or the enforcement of continuity conditions. Therefore, subdivision surface modeling has been increasingly adopted in high-end animation production and game engines and are provided as primitives in many popular modeling programs (e.g., Maya, Mirai, 3D Studio Max, Lightwave, etc.).
However, for many CAGD applications, subdivision surface modeling does not currently provide the necessary numerical exactness. Moreover, current trimming operations performed on such models frequently introduces unacceptable distortion, either because the operation does not guarantee substantially exact reproduction of the trim curve, or because the operation introduces unacceptable distortion in the area around the trim curve. The failure to reproduce the trim curve in the operation is especially problematic because it frequently introduces topological inconsistencies such as cracks during tessellation.
3. Related Applications.
This application is being filed concurrently with U.S. patent application Ser. No. 09/833,266, entitled “METHOD OF TRIMMING A REPRESENTATION OF AN OBJECT SURFACE COMPRISING A MESH OF TESSELLATED POLYGONS AND RELATED SYSTEM,” and U.S. patent application Ser. No. 09/833,627, entitled “DETAIL DATA PERTAINING TO THE SHAPE OF AN OBJECT SURFACE AND RELATED METHODS AND SYSTEMS,” both of which are owned in common by the assignee hereof, and both of which are hereby fully incorporated by reference herein as though set forth in full.